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DEFENDING  THE  BRIDE

 

 
Archimedes 3

Print Free Pamphlet - - Brief Summary

Why  153  Fish  in  John  21:11  ?

Sections :

Introduction
Church Fathers : Sts. Jerome, Augustine, Gregory the Great, Cyril A.
No Reason ?
Why Church Fathers’ Answers Could Not Be John’s
Problems with Square Root of 3 Answer
Context Points to the Answer : An Explanation That Works
Archimedes : Context of Time and Place
Greeks and Wisdom
Fish
Calculating the Measure of the Fish
John’s Purpose
Why Church Fathers Did Not (could not?) Give John’s Idea
Conclusion

Greeks and Wisdom

The Greeks excelled in natural wisdom.  The even looked to mathematical wisdom as the key on how to live.

Wikipedia
“Greek mathematicians lived in cities spread over the entire Eastern Mediterranean, from Italy to North Africa, but were united by culture and language.…
One of the most important characteristics of the Pythagorean order was that it maintained that the pursuit of philosophical and mathematical studies was a moral basis for the conduct of life. Indeed, the words philosophy (love of wisdom) and mathematics (that which is learned) are said to have been coined by Pythagoras.”
Wikipedia Source
 

 

Most of the Greeks probably would not have memorized Archimedes method for calculating Pi, but they would have learned about it and how it used 153.  153 would have been as easily as recognizable to them as 3.14 is to us.   
   
Objection:

If John was wanting to allude to Archimedes work on Pi,  π, and since Pi, is so important would it not have been better for John to have used the number 314 rather than the number 153 fish?

Answer:

1. Archimedes Contribution
2. No Decimal System Before AD 1100

1. Archimedes Contribution

The reasoning of this objection is based on a misunderstanding what Archimedes accomplished.  Civilizations had known about Pi for over a thousand years before Archimedes. 1 Kings 7:23 suggests that Pi is equal, appoxiamately, to 3.  One method of determining its value is to measure the circumference of a large circle and to divide it by the measurement of the diameter.  However, measurements are inherently inaccurate and subjective.  It is difficult to determine the accuracy of a measurement to three or more significant digits.  Besides, taking measurements is subjective. How does one prove one measurement is better than another without introducing a third measurement ?  Debating which measurement is better is subjective.

However, Archimedes new method did not involve taking any measurements.  It was pure mathematical calculations.  It was completely objective and easily verifiable. There was no subjective argument to dispute.  Therefore, the accuracy was easily verifiable.

So, it was not so much a particular value of Pi, but rather Archimedes’ method of calculating Pi that was truly remarkable.  And so John’s reference to 153 was his way of pointing to this ingenious method that Archimedes developed.

Archimedes computed upper and lower bounds of π by drawing a regular hexagon inside and outside of a circle, and successively doubling the number of sides until he reached a 96-sided regular polygon.  Using pure math he calculated the perimeters of these polygons in relation to the diameter. 

 

 

 

This polygonal algorithm was so ground breaking that it dominated for over 1,000 years. It enabled a person to calculate the value of π, Pi, with as much accuracy as one desired.

Ludolph van Ceulen, in 1596, in his book Van den Circkel ("On the Circle"), used essentially the same methods as those employed by Archimedes some seventeen hundred years earlier. He calculated Pi to 20 digits, and later expanded it to 35 digits.
See Wikipedia

So, the important contribution on the part of Archimedes and the Greeks was not so much a particular value for π as it was this the new method of calculating π , Pi. 

Therefore, it was easier for John to allude to Greek wisdom and to Archimedes’ new method by using 153 than by referring to π itself.

2. No Decimal System Before AD 1100

Also, it is important to note that the decimal system  (in America we use the decimal point) with which we use to denote fractions or portions between whole numbers did not come into the west until the 12th century with the introduction of the Indian numerals.  So, what Archimedes proved was that Pi was between

    

 Or

    

Only by using the more modern notation would we be able to write 

3.1429  >  π  >   3.1408

The sequence 314 is a number the Greeks would not have recognized at all. 

So, the use of 314 was not even an option for John.  If John had wanted to refer to Pi he would have been restricted to using one of the numbers that were known and used at the time which was one of the numbers used in the fractional forms of   22/7  or  223/71. 

The easiest and simplest method for John to allude to this new method for calculating Pi was to use the number “153”  as it was much more conspicuous and certainly repeated more often than one of the numbers 7, 22, 71, or 223. This should be seen as obvious when we consider its prominent use in Archimedes’ calculations.

As stated above, Archimedes arrived at these values for  π  by constructing a polygon inside and another outside of a given circle.

He constructed these polygons by using   30° - 60° - 90° Δ Triangles.  These triangles have unique properties.  The ratio of the length of one leg to the other is  3 : 1.  This made his calculations much easier. 

Archimedes used two approximations for the  3 , one greater than its value, and the other less. They are expressed as follows : 

 

 
 

Since this equation ends with the number 153, John was able to allude to Archimedes’ work, and therefore to his wisdom by using that number.

 

 

More Details :

See 
Recognizing 153
A simple overview on how easily the Greeks at the time of John, in Ephesus, would have easily made the connection between John's use of 153 and the allusion to Archimedes' work.

Plato and Archimedes' Solids

See a more detailed discussion on the importance of the number 153 in Greek culture.  Read :
The Number 153 Was Very Prominent and Recognizable in Ancient Greek Culture

 

Continue ...
Fish


 

 

Sections :

Introduction
Church Fathers : Sts. Jerome, Augustine, Gregory the Great, Cyril A.
No Reason ?
Why Church Fathers’ Answers Could Not Be John’s
Problems with Square Root of 3 Answer
Context Points to the Answer : An Explanation That Works
Archimedes : Context of Time and Place
Greeks and Wisdom
Fish
Calculating the Measure of the Fish
John’s Purpose
Why Church Fathers Did Not (could not?) Give John’s Idea
Conclusion

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